This internship is dedicated to the study of phase transitions in two-dimensional systems, with a specific focus on critical curves in lattice models and their scaling limits. These models intricately portray non-local phenomena such as the domain walls in a 2D ferromagnet, configurations of a polymer adhered to a surface, and the boundaries of percolation clusters.

In two dimensions extremely powerful and exact methods are available to address such questions : integrability, conformal field theory (CFT), Schramm-Loewener evolution (SLE)... This internship will focus on the CFT approach, and its connection with the underlying symmetry of the lattice model (via the periodic Temperley-Lieb algebra).